Nonlinear Mixed-Effects Height to Crown Base Model for Moso Bamboo (Phyllostachys heterocycla (Carr.) Mitford cv. Pubescens) in Eastern China

Round 1

Reviewer 1 Report

The work presents a development of nonlinear mixed-effects height to crown base (HCB) model using three predictor variables concerning Moso bamboo. The study concentrated on predictor variables like bamboo height, canopy density, and total basal area of all the bamboos with diameter larger than that of the subject bamboo. The topic is relevant, and the study was well organized and presented. There are only minor comments to be considered:

The Figure 1 maybe could be more illustrative for readers which are not familiar with the China geography.

The quality of figure 3 could be improved, specifically considering the resolution.

Why the three functions for HCB modeling presented in table 3 were chosen? I believe a discussion could be included in this important part of the work.

The contribution of the present work for the literature considering aspects like model efficiency could be more explored in the Discussion or Conclusion sections.

Author Response

Reviewer 1

Comments and Suggestions for Authors

The work presents a development of nonlinear mixed-effects height to crown base (HCB) model using three predictor variables concerning Moso bamboo. The study concentrated on predictor variables like bamboo height, canopy density, and total basal area of all the bamboos with diameter larger than that of the subject bamboo. The topic is relevant, and the study was well organized and presented. There are only minor comments to be considered:

The Figure 1 maybe could be more illustrative for readers which are not familiar with the China geography.

Response: Thanks for your advice. We modified this in the manuscript. See line 116-120.

As shown below:

Figure 1. Study area showing location of the sample plots.

Note: A, B, C, D, and E represents China, Jiangsu Province, Wuxi City, Yixing City and sample plot locations respectively.

 

The quality of figure 3 could be improved, specifically considering the resolution.

Response: thanks for your advice. We modified this in the manuscript. See line 122-123. As shown below:

Why the three functions for HCB modeling presented in table 3 were chosen? I believe a discussion could be included in this important part of the work.

Response: thanks for your advice. We modified this in the manuscript.

See line 322-330.

Due to the uncertainties and complexity of the growth processes of bamboo forests, we lacked an effective tool or method to determine a reasonable combination of variables (tree-level, stand-level, and climate) and their interactions with the stand-specific conditions for predicting HCB. HCB has a certain maximum growth, which could be represented by horizontal asymptote (maximum-bamboo height). In forestry, logistic and exponential functions are widely used in the forest mortality [24,25], height growth [32], and DBH growth [33,34], and so on. Therefore, this study selected three model forms that are commonly used in the previous modeling studies [10,28,29], and they all have horizontal asymptotes.

The contribution of the present work for the literature considering aspects like model efficiency could be more explored in the Discussion or Conclusion sections.

Response: thanks for your advice. We modified this in the manuscript.

See line 417-428.

At present, there are only a few studies on the HCB modeling, especially using the mixed-effects HCB modeling, which have also adopted various sampling strategies in calibration and identified an optimal size of sample for predicting HCB [11,20]. How-ever, most of these studies focused on arbor forest. Bamboo has unique characteristics, such as faster growth rate, shorter rotation, higher productivity, and more early maturation than other forestry crops. The greater HCB of bamboo, the higher would be the utilization efficiency of the bamboo culm [15-18]. Some studies have established bam-boo height-DBH models [3-5,27]. Because of measurement difficulty and higher cost of biomass sampling of bamboo forests, our model can be combined with existing bamboo height-DBH models for more accurately estimating biomass, and thus more precise es-timates of carbon storage can be obtained using the carbon conversion coefficients. These results may provide a good reference for bamboo forest management in the con-text of climate change. Our model is simpler to apply and can greatly reduce the work-load of forest survey.

 

 

Author Response File: Author Response.docx

Reviewer 2 Report

General comments

The manuscript “Nonlinear mixed-effects height to crown base model for Moso bamboo (Phyllostachys edulis) in eastern China” by Zhou et al. is an example of using a nonlinear mixed-effects modeling  as new tool to simulate height to crown base (HCB) based on bamboo height, canopy density, and total basal area of bamboo. The paper is well structured. The introduction provided a comprehensive overview of the background information and the pertinent literature, and it demonstrated the need for the current study. Material and Methods involved a description of different statistical techniques, included NLME approach, their using in the analysis as well as an information of study area and data used. In the Results the authors considered step-by-step different simulation approach (from simplest to most complex) to improve a forecast of HCD based on three allometric variables frequently used in forestry research. Based on it the authors provided a satisfactory discussion and made the corresponded conclusion

But there is an issue which should be considered in the MS. Theoretically  it is better to use as simple model as possible in case if further complication of the model cannot get a significant improvement of simulation. I really do not recognize the difference in RMSE, R2, etc between M4(M6) non-linear regressions with three parameters and M7(M8) NLME models which contains seven parameters included random error. What was a reason to select the  M7 and M8 as optimal models? Moreover NLME approach is parametric, which requires a certain distribution of predictors. Detailed clarifications are needed in the Results and Discussion.

I would suggest to publish the MS after major revision.

Specific comments

Lines 96-97: The annual (and summer ) total amount of precipitation should be added.

Figure 1: The figure contains three parts (from bigger territory to study sites). I would suggest to number those parts, to add latitudes and longitudes on common territory, to indicate 29 plots on study area, to add a corresponded description in figure capture.

Figure 2: It seems to me the Figure consists from three different pictures! Figure 2 and its description should be improved respectively.

Figure 3: In the capture it is not a ‘relationship’! The ‘relationship ‘ should be corrected on scatterplot.

By the way there are no any relationships between variables! If the authors have an opposite opinion they need to confirm it by the corresponded statistics and add it in the Results.

 

Line 129: Taking into account the importance of VIF statistics in further analysis I would suggest to describe it in more details.

Section 2.3.2 Matrix form of equations is convenient in program code. I would suggest to use a scalar form for better understanding of the Mixed-effects model approach.

Line 199: What was a criterion to use the 100 iterations? Are the 100 iterations enough to produce a robust results? Clarification is needed.

Lines 208-211: In the section 2.2. the authors wrote: ‘Collinearity between the predictor variables was analyzed using variance influence factor (VIF)’. What is a connection between ‘collinearity between independent (or predictor) variables’ and their contribution ‘to the HCB variations’? Clarification is needed!

Table 5. What was a reason to include DBH as a predictor and to consider three more modeling strategies (M4+,M5+,M6+) taking into account that VIF(DBH)=560 (see table 3)? Clarification is needed.

Figure 5. It seems to me the RMSE are statistically the same, and not depended on number of bamboo!

Line 311: The authors wrote: ‘In this study, CD was significantly correlated with HCB’. This expression is a contraversion of figure 3 where there is no relationship between HCD and CD (the corresponded scatterplot looks like random). Clarification is needed.

Author Response

Reviewer 2

Comments and Suggestions for Authors

General comments

The manuscript “Nonlinear mixed-effects height to crown base model for Moso bamboo (Phyllostachys edulis) in eastern China” by Zhou et al. is an example of using a nonlinear mixed-effects modeling as new tool to simulate height to crown base (HCB) based on bamboo height, canopy density, and total basal area of bamboo. The paper is well structured. The introduction provided a comprehensive overview of the background information and the pertinent literature, and it demonstrated the need for the current study. Material and Methods involved a description of different statistical techniques, included NLME approach, their using in the analysis as well as an information of study area and data used. In the Results the authors considered step-by-step different simulation approach (from simplest to most complex) to improve a forecast of HCD based on three allometric variables frequently used in forestry research. Based on it the authors provided a satisfactory discussion and made the corresponded conclusion

But there is an issue which should be considered in the MS. Theoretically it is better to use as simple model as possible in case if further complication of the model cannot get a significant improvement of simulation. I really do not recognize the difference in RMSE, R2, etc between M4(M6) non-linear regressions with three parameters and M7(M8) NLME models which contains seven parameters included random error. What was a reason to select the M7 and M8 as optimal models? Moreover NLME approach is parametric, which requires a certain distribution of predictors. Detailed clarifications are needed in the Results and Discussion.

Response：Thanks for your advice.

In this study, we first find the optimal basic model by comparing the basic models, and then introduce random effects. After introducing the random effect, one model is basically unchanged (M7), and the fitting index of the other model becomes better (M8). We added the content and method to the question and answer the result.

See line 194-200.

The best fitting base model with the selected predictor variables was used to formulate a one-level NLME HCB model by introducing sample plot-level random effects into the model. The NLME model alternatives that resulted from all the possible expansion combinations of fixed-effects parameters with the random effects were fit to the data. The resulting model with the smallest AIC, BIC and the largest log-likelihood (LL)was selected for further analyses. To avoid the problems due to over-parameterization, we performed likelihood-ratio test (LRT) [31].

Line 280-285

The AIC, BIC and -2log likelihood values of different models are shown in Table 8. The AIC, BIC and -2log likelihood calculated by the model with the random effects pa-rameters is smaller than that of the model fitted with the ordinary least square regres-sion method (also known as traditional modeling method). It indicates that adding random effects parameters does not lead to over parameterization, and could prove that the mixed-effects model was more appropriate than the traditional model for HCB modeling.

Line 372-379.

In this study, the over parameterization problem did not occur, and adding random effect parameters in the model produced better fitting effects than the model estimated with traditional modeling (Table 8). Introducing too many tree-level and stand-level variables may significantly improve the prediction accuracy of HCB model, but models might not be converged with global minimum, and estimated model could have large bias due to over parameterization [11,31]. In addition, adding many predictors to the HCB model will increase the cost of forest inventory. Therefore, a simple model with a reasonable accuracy is the first choice for effective forest management.

I would suggest to publish the MS after major revision.

Specific comments

Lines 96-97: The annual (and summer ) total amount of precipitation should be added.

Response: Thanks for your advice. We added this in the manuscript.

See Line 101-102.

The average annual precipitation is 1805.4 mm, and the summer precipitation ac-counts for half of the annual precipitation.

Figure 1: The figure contains three parts (from bigger territory to study sites). I would suggest to number those parts, to add latitudes and longitudes on common territory, to indicate 29 plots on study area, to add a corresponded description in figure capture.

Response: Thanks for your advice. We modified the Fig1 in the manuscript.

See line 116-120.

As shown below:

Figure 1. Study area showing location of the sample plots.

Note: A, B, C, D, and E represents China, Jiangsu Province, Wuxi City, Yixing City and sample plot locations respectively.

Figure 2: It seems to me the Figure consists from three different pictures! Figure 2 and its description should be improved respectively.

Response: Thanks for your advice. The purpose of adding Figure 2 is to let readers know what moso bamboo looks like.

We modified the Fig 2. and added some description in the manuscript.

See Line 114-116.

Figure 2 shows the characteristics of bamboo in this area (stand density is high and bamboo crown is not easy to distinguish), indicating the importance and urgency of building HCB model.

 

Figure 3: In the capture it is not a ‘relationship’! The ‘relationship ‘ should be corrected on scatterplot.

Response: Thanks for your advice. We modified this in the manuscript.

See Line 111-112.

Scatter plots distributions between height to crown base (HCB) and different predictor variables are shown in Fig. 3.

By the way there are no any relationships between variables! If the authors have an opposite opinion they need to confirm it by the corresponded statistics and add it in the Results.

Response: Thanks for your advice. We modified this in the manuscript.

We added the correlation value between HCB and different predictive variables in the Figure.

See Line 128-129.

r represents the correlation analysis between HCB and different variables, and the p value be-tween HCB and each variable is < 0.001).

Line 129: Taking into account the importance of VIF statistics in further analysis I would suggest to describe it in more details.

Response: Thanks for your advice. We modified this in the manuscript.

See Line 142-147.

Multicollinearity among the independent variables was verified with the variance inflation factor (VIF). According to a common rule-of-thumb, multicollinearity among variables was considered to occur when VIF > 5 [28]. Thus, the variance inflation fac-tor (VIF) was used to examine whether variables would be collinearity with each other, and variables with VIF < 5 were retained in our final models.

Section 2.3.2 Matrix form of equations is convenient in program code. I would suggest to use a scalar form for better understanding of the Mixed-effects model approach.

Response: Thanks for your advice. We added a paragraph to describe it, which makes it easier for readers to understand the mixed effect model. And I calculated the matrix form (see below). Since we compare different models, it is sufficient to introduce the method here, and the scalar form is not required.

See Line 181-185.

See for detailed explanation and calculation method [22,30].

Vector μi of the random effects (ui1, ui2, ui3) in these models (Eqs. M7 and M8) was assumed to have a multivariate normal distribution with zero mean and plot variance–covariance matrix D, defined by Eq. 6.

      

Line 199: What was a criterion to use the 100 iterations? Are the 100 iterations enough to produce a robust results? Clarification is needed.

Response: Thanks for your advice. We added this in the manuscript.

See Line 229-231.

Under the same sampling strategy mentioned above, some studies repeated 40 times and showed robust results [11,20,24]. In this case (though sample data used in the current study is relatively small), in order to ensure the stability of the results.

Lines 208-211: In the section 2.2. the authors wrote: ‘Collinearity between the predictor variables was analyzed using variance influence factor (VIF)’. What is a connection between ‘collinearity between independent (or predictor) variables’ and their contribution ‘to the HCB variations’? Clarification is needed!

Response: Thanks for your advice. The variables in the model must first ensure that there is no collinearity problem. When we evaluate the multicollinearity between variables, we take HCB as the dependent variable and six forest variables as the independent variable. The result of the study is that there is no collinearity among h, CD and BAL variables, combined with the scatter diagram distribution of various variables in Figure 3, these variables have a certain impact on the distribution of HCB.

We modified this in the manuscript.

See Line 241-245.

Only three variables were retained in the final NLME HCB model based on the VIF criterion (VIF < 5), which is commonly used for variable selection, such as bamboo height (H), canopy density (CD), and diameter larger than that of the subject bamboo individual (BAL) (Table 3). These three variables had significant contributions to the HCB variations (Fig. 3).

Table 5. What was a reason to include DBH as a predictor and to consider three more modeling strategies (M4+,M5+,M6+) taking into account that VIF(DBH)=560 (see table 3)? Clarification is needed.

Response: Thanks for your advice. We deleted this section. DBH is a reliable factor in forestry field investigation. The reason for DBH = 560 is the existence of BAL（BAL is calculated by DBH）. And the reason why BAL is better than DBH has also been discussed.

See Line 346-352.

Figure 5. It seems to me the RMSE are statistically the same, and not depended on number of bamboo!

Response: Thanks for your advice.

When increasing the number of samples, RMSE and TRE showed a downward trend. The purpose is to find a sampling method with the largest decline rate. The use of average DBH bamboo per sample plot led to the largest reduction in RMSE and TRE values.

And we also discussed the result in the discussion.

See Line 415-418.

RMSE are statistically identical (Fig. 5), which may be due to small number of bamboo individuals in each sample plot. However, when increasing the number of samples bamboos, RMSE and TRE showed a downward trend. Our study will provide a cost effective method of sample plot investigation in future.

Line 311: The authors wrote: ‘In this study, CD was significantly correlated with HCB’. This expression is a contraversion of figure 3 where there is no relationship between HCD and CD (the corresponded scatterplot looks like random). Clarification is needed.

Response: Thanks for your advice. We modified this in the manuscript.

See Line 354-357.

CD had a certain impact on HCB (Fig.3), and the parameter estimate of M8 was significantly negatively correlated (p < 0.05). (i.e. with larger CD, there would be smaller HCB). Notably, CD has not been used as a predictor in any previously developed HCB models, confirming the novelty or our study.

 

 

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

After the first round the authors followed all the recommendations and suggestions to improve the MS.

The MS can be published as it is.

Author Response

Thank you for your contribution to this manuscript.